Confidence interval for a churn rate

Question

Of 300 randomly sampled users, 45 churned this month. Construct a 95% confidence interval for the true churn rate.

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Setup. Use \hat{p} \pm z^{}\sqrt{\hat{p}(1-\hat{p})/n} with z^{} = 1.96. Here \hat{p} = 45/300 = 0.15. Compute. The standard error is \sqrt{\frac{0.15 	imes 0.85}{300}} = \sqrt{0.000425} = 0.0206. Margin of error = 1.96 	imes 0.0206 = 0.0404, so 0.15 \pm 0.0404 = [0.110,\ 0.190]. Interpret. With 95% confidence the true monthly churn is roughly 11% to 19%. The event count (45) is comfortably above the rule-of-thumb minimum of about 10, so the normal approximation is reasonable. Takeaway. For a proportion interval to be reliable you want at least about 10 successes and 10 failures; here both …

Confidence interval for a churn rate

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